Estimation of the proportion of diploid males in populations of hymenoptera

Abstract

Diploid males occur at low frequencies in natural populations of Hymenoptera as a consequence of the sex-determination system. Routine electrophoretic surveys will often reveal heterozygous diploid males. Maximum likelihood estimates are given for φ, the proportion of males in the population that are diploid, when data are available from males only or from both males and females. In the simplest case, using male data only, φ= B2/2pqT2, where p and q are the gene frequencies at the marker locus, B2 is the number of heterozygous diploid males and T2 is the total number of males sampled. The variance V(φ) = φ[1 -2pqφ-(1 - 4pq)φ2]/2pqT2. When both male and female data are available then φ, the proportion of diploids that are male, can also be estimated. This allows the approximate effective number of sex-determining alleles (assuming a single locus system) to be determined. Maximum likelihood estimates of φ have to be obtained numerically when data are available from multiple-allelic or multiple marker loci. © The Genetical Society of Great Britain.